Block #287,192

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 5:29:39 AM · Difficulty 9.9864 · 6,529,243 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

c342ff5b31ba7c1b09f9082549779b9c419914cabce49e9f5d58757b0680e606

View on Chainz ↗

Height

#287,192

Difficulty

9.986397

Transactions

Size

968 B

Version

Bits

09fc847f

Nonce

43,471

Timestamp

12/1/2013, 5:29:39 AM

Confirmations

6,529,243

Mined by

⛏️ aaR;MAQyr8Lw3A4nTbkdHcAPqKiPptkhs4nt3Pn

Merkle Root

f9bebcd31ac6d58160c5dbdee08b94901f4aa98efc4167eb2dbe31a01fcd6976

Transactions (1)

Coinbasef9bebcd31ac6d5…be31a01fcd6976

1 in → 24 out10.0100 XPM879 B

AQyr8Lw3…hs4nt3Pn Ad9pSzHt…cpJ3y2zz Ae58nAEb…GFUA15fv AZ2pPuKg…95SN2Yr7 Ac5sZcdP…kzV4eckG

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.338 × 10⁹¹(92-digit number)

53385516985976607304…47548521706219016639

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

5.338 × 10⁹¹(92-digit number)

53385516985976607304…47548521706219016639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.338 × 10⁹¹(92-digit number)

53385516985976607304…47548521706219016641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.067 × 10⁹²(93-digit number)

10677103397195321460…95097043412438033279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.067 × 10⁹²(93-digit number)

10677103397195321460…95097043412438033281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.135 × 10⁹²(93-digit number)

21354206794390642921…90194086824876066559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.135 × 10⁹²(93-digit number)

21354206794390642921…90194086824876066561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.270 × 10⁹²(93-digit number)

42708413588781285843…80388173649752133119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.270 × 10⁹²(93-digit number)

42708413588781285843…80388173649752133121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

8.541 × 10⁹²(93-digit number)

85416827177562571687…60776347299504266239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.541 × 10⁹²(93-digit number)

85416827177562571687…60776347299504266241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #287,192

Cookie Preferences